Prior to the present invention, formally-appearing dressy-type flat-top hats or caps to which the present invention is exclusively directed, have had solely an adjustable fitting of one sort or another, which have heretofore include unsightly open through-space holes extending between an overlapping portion and an overlapped portion of the heretofore discontinuous rim portion of the hat. As a result thereof, such prior art caps/hats have had a resulting non-fitting wrinkling and gapping-apart of these disconnected parts and have had considerable puckering in an unsightly manner; as a result thereof, the "fit" was not reliably adjustable nor snug. The prior type of adjusted flat-top hat also was not properly aligned with a resulting discomfort as well as unsightly in appearance. Such short comings heretofore reduced and often virtually destroyed any realistic utility and advantages purportedly achieved by the prior art adjustable hat or cap, the worn adjustable hat/cap having failed to holding its flat top and associated supporting rim in secure nor comfortable positions and manners, devoid of properly fitting thereof. Also, for flat-top dressy-type hats or caps having a reasonable degree of quality in the sense of having a turned-under band providing support to and as contrasted to the prior art hats having flimsy rims, there heretofore has not been a neat nor good-fitting relationship for adjustable-fit flat-top hats or caps having a turned-under supporting band because the turned-under band portion was heretofore unstable, such prior art adjustable-fit flat-top being not sewn-together and/or otherwise properly anchored, insofaras the turned-under support band that would overlap the inside of the other spaced-apart end of the discontinuous support band. The aforestated heretofore disadvantages reduced the value of the prior art adjustable flat-top dress-type hats because of their failure to properly operate or fit, as well as the resulting unacceptable unsightly appearance above-noted.
Additionally, as to the present inventors recent prior invention of the afore-mentioned parent application, while that invention constitutes a marked significant advance in the art as to quality caps and proper fitting thereof in alternative fitting for such adjustable-fit flat-top hat or cap for different head sizes, there never the less remained with that invention a twisting stress and unequal fitting on opposite sides of joined portions of the band and rim thereof as joined during adjustment to fit various head sizes. As well, the downwardly-extending seam at the normally rearwardly-positioned overlapped rim portions was slanted--i.e. normally not a vertical arrangement, and was not centered in the rear of the hat support rim, together with the resulting above-noted stress being greater in pull on one side of the cap as contrasted to an opposite other side of a flat-top hat or cap. These stresses also evidenced themselves in a wrinkling of the flat-top of the crown of the flat-top hat. In arriving at the present invention, other problems were encountered particularly with regard to distortion of the flat-top of the crown and/or its supporting rim, tending to prevent the flat-top from being a smooth even surface and tending to prevent the obtaining of equally stressed circumscribing portions of the top and of the supporting rim on which the flat-top is mounted.